upcoming events

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  • GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR
    The Yang-Mills Equations over Klein Surfaces

    3:30 PM-4:30 PM
    April 5, 2019
    1 Oxford Street, Cambridge, MA 02138 USA
    Abstract:

    In “The Yang-Mills equations over Riemann surfaces”, Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory, and derived results on topology of the moduli space of algebraic bundles over a complex algebraic curve. In this talk, I will discuss Yang-Mills functional over a Klein surface (a 2-manifold equipped with a dianalytic structure) from the point of view of Morse theory, and derive results on topology of the moduli space of real or quaternionic vector bundles over a real algebraic curve. This is based on joint work with Florent Schaffhauser.

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  • GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR
    Feral pseudoholomorphic curves and minimal sets

    3:30 PM-4:30 PM
    April 12, 2019
    1 Oxford Street, Cambridge, MA 02138 USA
    Abstract:

    I will discuss some recent joint work with Helmut Hofer, in which we define and establish properties of a new class of pseudoholomorhic curves (feral J-curves) to study certain divergence free flows in dimension three. In particular, we show that if H is a smooth, proper, Hamiltonian in R^4, then no regular non-empty energy level of H is minimal. That is, the flow of the associated Hamiltonian vector field has a trajectory which is not dense.

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  • GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR
    3:30 PM-4:30 PM
    April 19, 2019
    1 Oxford Street, Cambridge, MA 02138 USA
    Abstract:

    An exotic structure on a smooth manifold X is another smooth manifold which is homeomorphic but not diffeomorphic to X. There are many closed 4-manifolds which admit exotic smooth structures. However, it is still an open question whether there are exotic structures on simple closed 4-manifolds such as the 4-dimensional sphere (smooth Poincare conjecture) and S^1xS^3. Motivated by the latter case, Akbulut asked whether there are an integral homology sphere Y with non-trivial Rokhlin invariant and a simply connected homology cobordism from Y to itself. In this talk, I will introduce various invariants of homology cobordism classes of 3-manifolds and discuss some of their topological applications. In particular, we answer Akbulut’s question for various integral homology spheres and propose a plan to completely address his conjecture.

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  • GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR
    Heegaard Floer and homology cobordism

    3:30 PM-4:30 PM
    April 26, 2019
    1 Oxford Street, Cambridge, MA 02138 USA
    Abstract:

    We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains an infinite-rank subgroup and a Z-summand. The proof relies on the involutive Heegaard Floer homology package of Hendricks-Manolescu and Hendricks-Manolescu-Zemke. This is joint work with I. Dai, M. Stoffregen, and L. Truong.

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